Problem: Simplify the following expression and state the condition under which the simplification is valid: $x = \dfrac{p^2 + 20p + 100}{p^2 + 13p + 30}$
First factor the expressions in the numerator and denominator. $ \dfrac{p^2 + 20p + 100}{p^2 + 13p + 30} = \dfrac{(p + 10)(p + 10)}{(p + 3)(p + 10)} $ Notice that the term $(p + 10)$ appears in both the numerator and denominator. Dividing both the numerator and denominator by $(p + 10)$ gives: $x = \dfrac{p + 10}{p + 3}$ Since we divided by $(p + 10)$, $p \neq -10$. $x = \dfrac{p + 10}{p + 3}; \space p \neq -10$